Physics-informed deep learning reconstruction in medical imaging

Abstract

Background : Medical imaging techniques are widely used for detecting the whole or a certain part of the body in clinical applications. Mathematically, reconstruction of medical images can be solved through convex optimization algorithms based on relevant physical models. Specifically, the hyperpolarized 13C magnetic resonance spectroscopic imaging (MRSI), quantitative susceptibility mapping (QSM), and electrical impedance imaging (EIT) showed their promising applications, and their reconstructions are inverse problems, which are greatly dependent on inner physical principals. Recently, deep learning methods have also been incorporated in these reconstructions. But most of them lack the physical models in their structures, which would affect the reproducibility and accuracy when bias exist between testing data and training data. In contrary, physics-based deep learning reconstructions could greatly improve the generalizability and extend their applications, and four models were proposed for these imaging modalities. Methods : For hyperpolarized 13C MRSI, a deep learning prior was employed with the fidelity term to accelerate the reconstruction of MRSI. A two-site exchange model was used in simulating training data and testing cancer data. The reconstruction performance was improved for each group compared to those from zero-filled and compressed sensing with L1 regularization, which was further supported by peak signal-to-noise ratio (PSNR) results. This framework work accurately and robustly in 6 times acceleration, and even on dataset with 10% standard deviation noise. In the second part, a two-step deep-learning QSM pipeline consisting of two models, i.e. Projection onto convex set network (POCSnet1) and POCSnet2, was designed to decouple the trainable network components with spherical mean value (SMV) filters and dipole kernels. Our pipeline showed improved accuracy with normalized root mean square error (NRMSE) and high-frequency error norm (HFEN) for POCSnet2 are 58.1% and 56.7 on calculation of susceptibility through multiple orientation sampling (COSMOS) (N=1), and outperformed conventional deep learning models, i.e., biases < 3% vs. biases = 7-10%. This pipeline was extended into a Deep Learning-Regularized, Single-Step QSM model, Single-Step (SS)-POCSnet, in which the physical model based on a Single-Step model was iteratively applied with deep network regularizations. On synthetic datasets (N=10), SS-POCSnet showed the best performance, such as NRMSE is 37.3±4.2, and reduced the underestimation of susceptibility values in deep brain nuclei compared with other models considered. This model also performed well and improved accuracy in clinical dataset (N = 34). Finally, we proposed a cascaded cycle generative adversarial network (CycleGAN) model for the cross-modality of EIT to magnetic resonance imaging (MRI) on wrists. 713 EIT from 19 normal volunteers were acquired at three frequencies (70/140/200 kHz) and with paired 1.5T T1 weighted images. Compared with the end-to-end CycleGAN and Pix2Pix, proposed method achieved the best results in varied measurements in the MRI-style anatomical reference. The regularized EIT were reliable and accurate after employing the anatomical prior based on EIT physical model. Conclusion : The physics-informed deep learning methods showed their superiorities of accuracy and generalizability in medical image reconstructions, demonstrated on MRSI, QSM and EIT applications.